Simulation of an ECT Sensor to Inspect the Reinforcement of
Concrete Structures
Naasson P. de Alcantara Jr.*, Luiz Gonçalves Jr.
São Paulo State University – Unesp. Department of Electrical Engineering
*Av. Luiz E. C. Coube, 14-03, Bauru,SP, Brazil. naasson@feb.unesp.br
Abstract: This paper describes the use of
COMSOL Multiphysics to simulate an ECT
(Eddy Current Testing) sensor, designed to
inspect the elements of the reinforcement of
concrete structures. The electromagnetic parts of
the sensor constitute a RLC series circuit, where
L is the inductance of a multi-turn coil, R is the
total resistance, (the coil resistance and an
external one), and C is an external capacitance.
The paper describes the steps for the COMSOL
simulation. Simulations were done for three
configurations of the sensor, and the results will
be presented graphically.
Keywords: Concrete structures, Non-destructive
evaluation, Eddy current testing, Finite element
method, COMSOL Multiphysics.
1. Introduction
Due to its high plasticity, high load-carrying
capacity and low-maintenance requirements,
rebar-reinforced concrete is used in almost all
civil structures including commercial, industrial
and residential buildings, dams, power plants,
bridges, stadiums etc. Its high strength,
durability, sustainability and flexibility allow to
produce the most complex shapes of concrete
structures. However, although reinforced
concrete is a relatively durable and robust
constructional material, its performance can
decline dramatically over time. When exposed to
adverse
physio-chemical
environmental
conditions may lead to premature loss of strength
due to corrosion of rebar. These defects can
result in catastrophic structural failure unless
their presence is detected and their effects are
assessed in time. To keep a high level of
structural safety, durability and performance of
concrete structures, efficient systems for early
and regular structural assessment is mandatory.
The quality assurance during and after the
construction
of
new
structures,
after
reconstruction processes, as well as the
characterization of material properties and
damage as a function of time and environmental
influences, is a serious concern.
As a contribution to the theme, this paper
focuses on the use of eddy current NDT
techniques to inspect the reinforcement of
concrete structures.
Eddy current methods can be used to analyze
conductive materials through electromagnetic
induction. The probe device itself is nothing
more than an AC transformer. Eddy Current
probes work based on the following basic
electromagnetic concepts: 1) Current flow in a
coil generates a magnetic field. 2) A magnetic
field in proximity to a conductor produces an
electromotive force (in Volts), in the conductor.
If the conductor is a closed circuit, a current (in
Amperes) will flow. This current will produce an
opposite magnetic field that will react against the
variation of the original magnetic field. In the
case of solid conductor materials, eddy current
loops will appear within it. Eddy current
measurement consists of five steps: 1) Signal
excitation. 2) Material interaction. 3) Signal
pickup. 4) Signal conditioning and display. 4)
Analysis.
The use ECT in the identification of the
reinforcement of concrete structures has been
present in the related literature [1], [2], [3]. In a
previous paper [4], the first author of the present
paper built differential electromagnetic sensors,
produced dozens of reinforced concrete samples,
and performed laboratory tests. The results were
used to construct ANN training vectors, in order
to locate and identify steel bars under the
concrete cover.
In this paper, COMSOL Multiphysics [5]
will be used to simulate a new kind of ECT
sensor, designed to inspect the elements of the
reinforcement of concrete structures. The sensor
is, basically, a RLC series circuit, whose basic
principles will be described in the next section.
2. Description and Mathematical Basics of
the Proposed ECT Sensor
The sensors proposed in this work are,
basically, RLC circuits, where L is the
inductance of a multi-turn coil, Lc, R is the sum
of the coil resistance Rc and any other additional
Excerpt from the Proceedings of the 2015 COMSOL Conference in Curitiba
resistance, Re, and C is the capacitance of an
external capacitor, Ce, connected in series with
the coil. Figure 2 shows an equivalent electrical
circuit of the sensor.
Rc + jωLc
1/ jωCe
Re
Vc
A 3D model was developed, using COMSOL
Multiphysics. The first step was to define
Magnetic Field and Electrical Circuit as the
physics of the problem, and frequency domain
for the type of solution.
The next step was to model the ECT sensor.
A multi-turn coil, a ferrite box surrounding the
coil, and an aluminum box, to provide the
external shielding for the sensor, will constitute
it. Figure 2 shows, in a exploited way, the
components of the sensor.
~
Vsource
Figure 1. An electrical circuit of the ECT sensor for
reinforcement inspections.
Vsource is the voltage applied at the terminals
of the sensor, and Vc is the voltage measured
across the capacitor terminals. Using the
Kirchoff’s second law, Vsource and Vc can be
expressed as:
(1)
and
(2)
where R = Re + Rc, and the indexes are
suppressed. Expliciting the current in equation
(1), substituting in equation (2), and developing
algebraically, the voltage at the terminals of the
capacitor can be expressed as:
(3
)
At the resonant frequency, ωL = 1/(ωC), and
equation (3) is drastically reduced.
3. Use of COMSOL Multiphysics
3.1 Constructing the Model
Figure 2. The elements of the ECT sensor. From
bottom to top: the steel bar, multi-turn coil, ferrite box
and aluminum box.
These components were defined using the
options of the Geometry tool bar of COMSOL.
Using the Explicit option of the Definition tool
bar, the dominions were assigned as: Steel bar,
Coil, Ferrite box, Shielding and Air. After, the
materials were defined using the built in material
library (Air, structural steel, Ferrite and
Aluminum), and the characteristics of the multiturn coil was set (Coil type: Numeric, Coil
excitation: current, Number of turns: 800, coil
conductivity 5.8×107 S/m, and 24 AWG). As the
Magnetic Field physics interface was used,
Ampere’s Law and Initial Values conditions
were naturally imposed. Finally, magnetic
Insulation was applied to the boundaries of the
coil.
Meshing was chosen according to the regions
of interest, using predefined size options. Coarse
to the air up to extra fine, to the shielding. Free
tetrahedral elements were used. No special
features, like sweep and boundary layers were
necessary. Figure 3 shows the generated mesh,
hiding the air discretization.
3.2 Running COMSOL to Compare the
Magnetic Flux Behavior for Some Sensor
Configurations
Excerpt from the Proceedings of the 2015 COMSOL Conference in Curitiba
After to establish the model, the simulation
was done. Three configurations were considered
for the sensor:
1. The sensor is built using only the coil, without
the ferrite box and the aluminum shielding.
2. The sensor is built using the coil and the
ferrite box, but without the aluminum
shielding.
3. The sensor is built in its complete
configuration (all the elements are present: the
coil, the ferrite box and the aluminum
shielding).
In all three cases, a source voltage of 3.53
Vrms (10 Vpp) was considered. This value is not
relevant because the inductance is not dependent
on the level of excitation in cases such as these.
The magnetic materials present in the system
will never work close to their saturation levels.
Case 1: Figures 4 and 5 shows the magnetic
flux density norm at the surfaces of the coil and
the steel bar, when it is positioned at 20 mm
bellow the center of the sensor, as well in regions
where would be placed the ferrite box.
Figure 4. Magnetic flux density at the coil and steel
bar surfaces, and within regions that would be
occupied by the surrounding ferrite box (top
perspective), Legends, from left to right: ferrite box
regions (twice), coil and steel bar.
Figure 3. Generated mesh for the model.
Before to start the simulations with the presence
of the steel bar under the sensor, initial
simulations were done in order to calculate the
inductance of the coil in each case. The presence
of materials like ferrite and aluminum in the
sensor affects significantly the resultant
inductance of the coil, and the use of the
COMSOL allows the calculation of this
parameter with a high level of reality. The results
for these initial simulations are summarized in
table 1.
Table 1: Inductances of the sensor at no-load
Case 1
Case 2
Case 3
frequency
8.15 kHz
7.00 kHz
7.00 kHz
inductance
70.65 mH
102.43 mH
90.92 mH
Figure 5. Magnetic flux density at the coil and steel
bar surfaces and within regions that would be
occupied by the surrounding ferrite box (bottom
perspective). Legends are the same as figure 4
Figures 6 and 7 show details of the eddy
current induced within the steel bar.
The important information that can be
obtained from these graphics is the following. 1)
The values of magnetic induction in the materials
are very low, ensuring that the sensor will
always operate in the linear region, with respect
to the magnetic field. 2) Eddy current will be
Excerpt from the Proceedings of the 2015 COMSOL Conference in Curitiba
induced in the bar portion that is right under the
sensor, and it is important in order to decide
which will be the size of its coverage upon the
bar.
signal variations can be observed. In addition,
the presence of the ferrite box surrounding the
coil causes an increasing by a factor of ten in the
magnetic field density in the region close to the
winding. In other words, again is possible to see
a better coupling between the magnetic flux and
the steel bar.
Figure 6. Eddy current induced within the steel bar.
Figure 9. Magnetic flux density at the coil and steel
bar surfaces, and within the walls of the ferrite box
(perspective from the bottom). Legends, from left to
right: ferrite upper wall and right wall, coil and steel
bar.
Figure 7. Eddy current induced within the steel bar.
Case 2: Figures 8 and 9 shows the magnetic
flux density norm at the surfaces of the coil and
the steel bar, and within the walls of the ferrite
box.
Figure 8. Magnetic flux density at the coil and steel
bar surfaces, and within the walls of the ferrite box
(perspective from the top). Legends, from left to right:
ferrite upper wall and right wall, coil and steel bar.
Comparing figures 4 and 8 is possible to
conclude that the maximum value of magnetic
flux density at the steel bar is increased about
28% in relation to the case 1. This conclusion is
very important, because the higher the flux
density, the greater will be the amount of energy
transferred to the bar, and therefore greater
Case 3: Figure 10 shows the magnetic flux
density norm at the surfaces of the coil and the
steel bar, and within the walls of the aluminum
box.
Figure 10. Magnetic flux density at the coil and steel
bar surfaces, and within the walls of the aluminum box
(perspective from the bottom). Legends, from left to
right: aluminum upper wall and right wall, coil and
steel bar.
In this case, it is easy to see that the magnetic
flux density within the aluminum box is very
close to zero. The ferrite box only is sufficient to
act as a shielding for the sensor.
3.3 Running COMSOL to Simulate the Sensor
Movement over the Steel Bar
COMSOL Multiphysics was used to simulate
the sensor movement over the steel bar, for the
Excerpt from the Proceedings of the 2015 COMSOL Conference in Curitiba
three configurations presented in the previous
subsection. Figure 11 represents the position of
the steel bar in relation to the sensor.
The best results are those for the case 2
configuration, and agree with the observations
made for the results presented in the previous
subsection.
4. Conclusions
h
d
Figure 11. Schematic representation of the sensor
position in relation to the steel bar.
In figure 11, h is the distance between the top
of the bar and the base of the sensor and d is the
distance between the center of the bar and the
axis of the sensor.
The gauge of the steel bar used in the
simulation is 10 mm. Six values for the
horizontal displacement (d = 100, 80, 60, 40, 20
and 0 mm), and two values for vertical position
(h = 10 and 20 mm) were considered. Figure 12
shows the results.
Figure 11. Obtained results for the three sensor
configurations, in function of the position of the
sensor.
In figure 12, black curves are the results for
the case 1 simulation; red curves are the results
for case 2 and blue curves the results for case 2.
Red marks are the results for h = 10 mm and
circle marks the results for h = 20 mm. The input
voltage was set to produce approximately 10 V
in each sensor configuration, at no load
condition.
This paper described the use of COMSOL
Multiphysics to model the electromagnetic parts
of an ECT sensor, designed to inspect the
armature elements of reinforced concrete
structure. Three models for the sensor were
proposed, and analyzed, based on finite element
simulations, with regard to their electromagnetic
behavior. The performance of the sensors were
also simulated and the results were satisfactory
in all the cases, but with advantages for the
configuration discussed in the case 2 (The use of
a ferrite box surrounding the sensor coil, but
without an external aluminum shielding).
COMSOL Multiphysics proved to be very useful
in the three-dimensional modeling of
electromagnetic components of this type of
application, and the results are very encouraging
for future works.
5. References
1. Yokota, O., Study of Reinforcing Bars
Detection Buried in Concrete Structures Using
Eddy Current Method, in: 15th WCNDT-World
Congress on Non-destructive Testin, (2000),
available online www.ndt.net/article/wcndt00/,
(accessed on 31/08/2015)
2. Pudov, V., Electromagnetic Devices for the
assessment of the State of Reinforcement
Elements in Reinforced Concrete Structures,
Russian J. of Non-destructive Testing, 42, 26-37
(2006)
3. Rubinacci, G., Tamburino, A., Ventre, S., Int.
J. of Applied Electromagnetic and Mechanics,
25, 333-339, (2005)
4. Alcantara Jr., N. P, Identification of Steel Bars
Immersed in Reinforced Concrete Based on
Experimental Results of Eddy Current Testing
and Artificial Neural Network Analysis,
Nondestructive Testing and Evaluation, 28, 5871 (2013)
5. COMSOL Multiphysis, Avaliable online,
http://comsol.com, (accessed on 20/09/2015).
Excerpt from the Proceedings of the 2015 COMSOL Conference in Curitiba
6. Acknowledgments
The authors express their gratitude to the
FAPESP – São Paulo Research Foundation, for
the financial support of this research, under the
grants number 2014/08797-8.
Excerpt from the Proceedings of the 2015 COMSOL Conference in Curitiba